It is easy for Apple employees to tell when they have lost the attention of Eddy Cue, the leader of the company’s sprawling internet initiatives—from its music and video businesses to its maps service.

casual men's shoes sneakers man flats Men's printing flower flower sho Fengnong During meetings, Mr. Cue is sometimes known to fall silent, shut his eyes and tilt his head back, leaving other participants to wonder whether he is staring at the ceiling or sleeping, said several former Apple employees and one outside partner present on multiple occasions when it happened over the past few years. In at least two of these situations, Mr. Cue began snoring, one source said.